A364131 Numbers k for which A348717(k) is a multiple of A348717(sigma(k)).

1, 2, 4, 9, 16, 25, 64, 81, 289, 324, 400, 484, 729, 1681, 2401, 3481, 4096, 5041, 7921, 10201, 15625, 17161, 27889, 28561, 29929, 39204, 65536, 83521, 85849, 146689, 262144, 279841, 458329, 491401, 531441, 552049, 579121, 597529, 683929, 703921, 707281, 734449, 829921, 1190281, 1203409, 1352569, 1394761, 1423249, 1481089

Offset: 1

Author

Antti Karttunen, Jul 11 2023

Keywords

• nonn

Comments

Conjecture: All terms apart from a(2) = 2 are squares.

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A008848, A023194 (subsequence), A348717, A350072.

Programs

PARI

A348717(n) = { my(f=factor(n)); if(#f~>0, my(pi1=primepi(f[1, 1])); for(k=1, #f~, f[k, 1] = prime(primepi(f[k, 1])-pi1+1))); factorback(f); }; \\ From A348717
isA364131(n) = !(A348717(n)%A348717(sigma(n)));